Each time they pay out, they have to either live with the reduction of budget, or they have to propose an additional levy. To propose the additional levy usually requires a vote, and political ramifications. They can't just raise taxes willy nilly. Eventually, the mayor, or his/her replacement will fire the police chief and possibly some of the officers. It has ramifications to them also, it isn't just a "people's" money ordeal. You know a mayor can't just go ask for money without an explanation, and if that mayor has to explain why the police force needs more money, in a public forum, chances are, he/she will be rebutted by the other side.
I mean think about it, even many of the "school levies" aren't passing. The "for the kids" argument isn't even working anymore.